A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn.
1. What is the probability of selecting a purple marble and then a white marble?
2. What is the probability of selecting two white marbles?
3. Is there a greater chance of selecting two white marbles in a row or two purple marbles in a row?
Is this the answer: 1. Pr(p, w)=7/9*2/8
2. pr(w,w)=2/9, 1/8
3. obviously, purple then purple is greatest chance
Pr(p,p)=7/9,6/8
Pr(w,w)=2/9,1/8
1. correct if you reduce it to 7/36
2. prob(2whites) = (2/9)(1/8) = 1/36
3. prob(2 purples) = (7/9)(6/8) = 7/12
so what do you think when comparing 1/36 with 7/12 ?
1. To find the probability of selecting a purple marble and then a white marble, we need to multiply the probability of selecting a purple marble from the bag without replacement by the probability of selecting a white marble from the remaining marbles. The probability of selecting a purple marble on the first draw is 7/9 since there are 7 purple marbles out of a total of 9 marbles. After removing the first marble, there are now 8 marbles left in the bag, with 2 white marbles. Therefore, the probability of selecting a white marble on the second draw is 2/8. To find the total probability, we multiply these probabilities: Pr(p, w) = (7/9) * (2/8).
2. The probability of selecting two white marbles can be found by multiplying the probability of selecting a white marble on the first draw by the probability of selecting another white marble on the second draw. The probability of selecting a white marble on the first draw is 2/9 since there are 2 white marbles out of a total of 9 marbles. After removing the first marble, there are now 8 marbles left in the bag, with 1 white marble. Therefore, the probability of selecting another white marble on the second draw is 1/8. To find the total probability, we multiply these probabilities: Pr(w, w) = (2/9) * (1/8).
3. To determine which has a greater chance, we compare the probabilities calculated in question 2 and question 3. From the calculations, Pr(p, p) = (7/9) * (6/8) and Pr(w, w) = (2/9) * (1/8). By comparing these probabilities, we can see that the probability of selecting two purple marbles in a row is greater than the probability of selecting two white marbles in a row.